These general properties have an immediate consequence: they allow one to introduce the notion of the main check-operator [1]}, [2]}. Indeed, one can construct the resolvent from the free energy not only by the standard loop operator \(\hat{\nabla }_z(t)\)  acting on \(t_k\) 's, but also by a check-operator acting on the moduli \(T_k\) :
\(\rho ^{(1)}(z)=\hat{\nabla }_z(t){\cal F}=\check{\nabla }_z(T){\cal F}.\) 
